Opthalmic lens for use in the correction of astigmatism

ABSTRACT

An ophthalmic lens for use in the correction of astigmation, wherein in order to reduce the critical thickness and/or the variation of the edge thickness along the circumference of the lens, the refractive index changes at least along the critical main section in such a manner that at least part of the cylindrical correction is attained by the refractive index variation.

FIELD OF THE INVENTION

The present invention relates to an ophthalmic lens for use in thecorrection of astigmatism.

STATE OF THE ART

Ophthalmic lenses with astigmatic action usually have a spherical and atoric surface. Lenses of this kind have a number of disadvantages:

Aberrations are only optimumly corrected for the vertex of the lens,while increasing along the main sections as well as between the mainsections toward the edge. In lenses of positive power, center thicknessis very great and in lenses of negative power, the thickness of the edgeis quite great, moreover, the edge thickness varies along thecircumference of the lens due to the toricity of the lens, the latterbeing extremely bothersome in lenses in so-called rimless frames.

Furthermore, if there is a marked difference in sight impairment betweenthe two eyes, the two lenses will also differ considerably inappearance.

Although aberrations may be diminished by means of aspherical mainsections, by way of illustration conical sections, the reduction inthickness that can be achieved is rather minimal.

DESCRIPTION OF THE INVENTION

The object of the present invention is to provide an ophthalmic lens foruse in the correction of astigmatism, in which the critical thickness,i.e. the center thickness in the case of lenses of positive power andthe thickness of the edge in the case of lenses of negative power and/orthe variation in the edge thickness along the circumference of the lens,is substantially reduced compared to the state of the art.

An inventive solution to the foregoing object and its furtherembodiments are set forth in the claims hereto:

In accordance with the present invention it was understood that aconsiderable reduction in the critical thickness and/or the variation ofthe edge thickness along the circumference of the lens can be attainedby changing the refractive index in the case of plus lenses at leastalong the stronger refracting main section and in the case of minuslenses at least along the lower refracting main section so that at leastpart of the cylindrical correction is achieved by changing therefractive index. As in plus lenses, the critical thickness, that is thecenter thickness or the edge thickness, is determined by the higherrefracting main section and in minus lenses by the (in a mathematicalsense) lower refracting main section hereinafter this main section willbe called the critical main section. Accordingly the other main sectionwill be called the non-critical main section.

Of course, it is also possible within the scope of the inventive conceptto change the refractive index in the direction of the other mainsection and/or in the direction of the optical axis of the lens inaddition to changing the refractive index along the critical mainsection. In this manner, aberrations can be kept at a minimum over theentire ophthalmic lens.

In any event, it is, however, advantageous if the change in therefractive index along the (in a mathematical sense) lower refractingmain section is mirror symmetrical to the plane of the second(non-critical) main section.

In most cases of utilization, however, the further embodiment in whichthe refractive index only changes along the critical main sectionsuffices completely. Strikingly, it is not only possible to reduce thecritical thickness considerably with such asimple--one-dimensional--variation of the refractive index, but it isalso possible to maintain specific predetermined conditions regardingimage properties and, in particular, the quantity of the aberrationsalong the critical main section, i.e. it is possible to maintain two oreven more quantities under predetermined restrictions by changing asingle parameter.

Furthermore, the one-dimensional design of the gradient of therefractive index has the advantage that it can be produced comparativelysimply. Nonetheless, such a one-dimensional gradient has not hithertobeen considered in the relative literature. With regard to this,reference is made to, by way of illustration, the survey "TechnologicalTrends-Gradient Index Optics" in Photonics Spectra, March 1987, p. 71ffand especially to the section on p. 71 "Types of Gradients".

Complete elimination of the variation of the edge thickness and at thesame time a very sizable reduction of the critical thickness, i.e. thecenter thickness in lenses of positive power amd the edge thickness inlenses of negative power or both quantities in lenses in which a mainsection has positive power and a main section has negative power isyielded by the further embodiment in which the up to medium cylindricalcorrection, i.e. cylindrical correction ranging approximately between2-3 dpt., is solely achieved by changing the refractive index. In thismanner, namely, it is possible to utilize lenses with rotationallysymmetrical surfaces so that no variation of the edge thickness canoccur.

Aspheric surfaces may, naturally, be employed as rotationallysymmetrical surfaces, being preferred, by way of illustration, in thecase of major corrections for in that event the critical thickness and,particularly, the center thickness in lenses of positive power can bereduced considerably. Moreover, aberrations can at least besubstantially reduced along both main sections by using asphericrotationally symmetrical surfaces. Furthermore, atoric surfaces may alsobe used. i.e. surfaces deviating from the toric form and in which atleast one main section is aspheric in design.

In many possible applications it is, however, quite sufficient if bothsurfaces are spherical surfaces hereto.

Further, the present invention provides for a suitable a dimension forthe refractive index or refractive index change in the immediatevicinity of the optical axis.

BRIEF DESCRIPTION OF THE DRAWING

The present invention is made more apparent in the following sectionusing preferred embodiments with reference to the accompanying drawing,in which:

FIG. 1 shows a lens section,

FIG. 2 shows the course of the refractive index,

FIGS. 3 to 6 show the astigmatic deviation and the focussing error for aprior art ophthalmic lens having a cylindrical correction of +2 dpt.,

FIGS. 7a and 7b show a lens section,

FIGS. 8a and 8b show the change in the refractive index,

FIGS. 9 to 12 show the astigmatic deviation and the focussing error foran invented ophthalmic lens having a cylindrical correction of +2 dpt.,

FIG. 13 shows a lens section,

FIG. 14 shows the change in the refractive index,

FIGS. 15 to 18 show the astigmatic deviation and the focussing error fora prior art ophthalmic lens having a cylindrical correction of +4 dpt.,

FIGS. 19a and b show a lens section,

FIGS. 20a and b show the change in the refractive index,

FIGS. 21 to 24 show the astigmatic deviation and the focussing error fora first preferred embodiment having a cylindrical correction of +4 dpt.,

FIGS. 25a and b show a lens section,

FIGS. 26a and b show the change in the refractive index,

FIGS. 27 to 30 show the astigmatic deviation and the focussing error fora second preferred embodiment having a cylindrical correction of +4 dpt.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

All the figures are based on a system of coordinates in which the x-axisruns horizontally and the y-axis runs vertically. The origin of thecoordinate system lies in the geometrical center of the lens.

The angle σ' is the so-called eye facing angle of vision, in other wordsthe half aperature angle of the cone of vision.

The angle φ is a polar angle (azimuth angle), in which:

x-axis: φ=0°,

y-axis: =90°;

In FIGS. 1, 7a and 7 b, 13, 19a and 19b as well as 25a and 25 illustratesections of the respective ophthalmic lens for section planes φ=0° and90° and sometimes also for =45°. These sections are designated 0°, 45°,90° respectively.

FIGS. 2, 8a and 8b, 14, 20a and 20b as well as 26a and 26b depict thecourse of the refractive index n on the abscissa as a function of thedistance plotted on the ordinate in the respective section plane φ=constseen in this figure as a function of the angle σ' or as a function ofthe angle φ (ordinate) for the section planes φ=const. In the case ofthe figures having =const the ordinate of these figures is also theordinate for the "lens section" shown on the left.

The curves showing the refractive index are corresponding-to designated0°, 45°, 90° for the section plane φ=0°, 45°, 90° or with σ'=30° if theangle σ' is maintained constant.

FIGS. 3-6, 9-12, 15-18, 21-24 and 27-30 illustrate the astigmaticdeviation S' (unbroken lines) and the focussing error R (broken lines),i.e. the mean deviation from the prescription value, of the systemophthalmic lens/eye in centering with a distance eye center of rotationpoint/back vertex of the lens b'=28 mm, whereby the optical eye centerof rotation lies on the optical axis of the lens.

Furthermore, in calculating the curves it was assumed that the"cylindrical axis" of the eye in resting position lies in the x-axisonly moving parallel to the horizontal plane during vision motion. Ofcourse, other "eye models" may also be used as the basis for calculatingthe eye/ophthalmic lens system, by way of illustration the Listingprinciple, whereby partially better results are received for theinvented lenses, i.e. smaller values for the astigmatic deviation S' andfocussing error R.

FIGS. 1 to 6 show a customary ophthalmic lens with a cylindricalcorrection of +2 dpt and a cylindrical axis of (φ=) 0° as well as auniform refractive index n=1.525.

The front surface is a barrel-shaped torus having a vertex refractivepower D_(ji) =(n-1)/r_(ji), whereby r_(ji) is the radius of curvature ofthe surface j in the section i.

D_(1x) =6.75 dpt.

D_(1y) =8.59 dpt.

The surface facing the eye is - as in all the preferred embodimentsdescribed hereinafter - a spherical surface with

    D.sub.2x =D.sub.2y =-2.00 dpt.

If such an ophthalmic lens has a diameter of 66 mm and a

mimimum edge thickness of 0.50 mm

its maximum edge thickness is 2.8 mm

and its center thickness 8.09 mm.

Thus the ophthalmic lens has a spherical correction of 5.0 dpt and acylindrical correction of +2.00 dpt with an axis of 0°.

FIGS. 7 to 12 depict an ophthalmic lens of the invention having acylindrical correction of +2 dpt and a cylindrical axis of (φ=) 0° aswell as a changing refractive index in accordance with the presentinvention, the variation of which is depicted in FIG. 8 for variousvalues of φ or σ'.

The front surface as well as the surface facing the eye are sphericalsurfaces with a vertex refractive power D

    D.sub.1x =D.sub.1y =6.82 dpt.

    D.sub.2x =D.sub.2y =-2.00 dpt.

The cylindrical correction is produced by changing the refractive indexn, which is a function of y.

If such an ophthalmic lens has a diameter of 66 mm

and a uniform edge thickness of 0.50 mm

its center thickness is 5.85 mm.

A comparison of the invented ophthalmic lens and a customary lensreveals the following:

The center thickness, i.e. the critical thickness in an ophthalmic lensof positive power is reduced by approximately 27% and the maximum edgethickness by approximately 80% without worsening the aberrations. On thecontrary, compared to a customary toric lens with a spherical mainsection, the invented ophthalmic lens has even more advantageous imageproperties. In particular, the focussing error R does not acquire anypositive values worth mentioning, thus can be compensated for bynegligible adaption.

Furthemore, a comparison of FIG. 12 with FIG. 6, which show theaberrations on a cone with a constant angle of vision σ', reveals thatthe invented ophthalmic lens has substantially better image properties.

It is particularly remarkable, however, that, despite the utilization ofonly one-dimensional gradients of the refractive index and consequentlyrestricted possibilities of variation in correction, it possible tomaintain specific marginal conditions for aberrations in addition tomeeting the restrictions regarding to center and edge thickness:

In the ophthalmic lens of the present invention illustrated in FIGS. 7to 12, the error correction is designed in such a manner that for φ=0°the focussing error R and for φ=90° astigmatism S' are approximatelyzero up to the angles of vision σ'=30°.

The calculation of the one-dimensional gradients of the refractive indexn(y) is attained with spline functions in the illustrated preferredembodiment, the exact course is indicated in FIGS. 8a and 8b. If therefractive index n(y) attained by spline functions is approximated inthe region of the optical axis with a Taylor series

    n(y)=n.sub.o +n.sub.2y *y.sup.2 +. . .

the coefficient yielded is

    n.sub.2y =-1.661*10.sup.-4 [mm.sup.-2 ].

FIGS. 13 to 18 depict another customary ophthalmic lens having acylindrical correction of +4 dpt and a cylindrical axis of (φ=) 0° aswell as a uniform refractive index n=1.525.

The front surface is a barrel-shaped torus with a vertex refractivepower D

D_(1x) =6.68 dpt.

D_(1y) =10.23 dpt.

The eye-facing surface is a spherical surface with

    D.sub.2x =D.sub.2y =-2.00 dpt.

If such an ophthalmic lens has a diameter of 66 mm

and a minimum edge thickness of 0.50 mm

its maximum edge thickness is 5.25 mm

and its center thickness 10.43 mm.

Thus the ophthalmic lens has a spherical correction of 5.0 dpt and acylindrical correction of +4.00 dpt at an axial position of 0°.

FIGS. 19 to 24 show a first preferred embodiment of an inventedophthalmic lens having a cylindrical correction of +4 dpt and acylindrical axis of (φ=) 0° as well as a changing refractive index inaccordance with the present invention, the variation of which isdepicted in FIG. 20.

Both the front surface and the eye-facing surface are spherical surfaceswith a vertex refractive power of D

    D.sub.1x =D.sub.1y =6.82 dpt.

    D.sub.2y =D.sub.2y =-2.00 dpt.

The cylindrical correction is produced by changing the refractive indexn, which is a function of y.

If such an ophthalmic lens has a diameter of 66 mm

and a uniform edge thickness of 0.50 mm,

the center thickness is 5.85 mm.

FIGS. 25 to 30 show a second preferred embodiment of the ophthalmic lensof the present invention having a cylindrical correction of +4 dpt and acylindrical axis of (φ=) 0° as well as also with a refractive indexchanging in accordance with the present invention, the variation ofwhich is depicted in FIG. 26.

The front surface is a barrel-shaped torus having a vertex refractivepower D

D_(1x) =6.75 dpt.

D_(1y) =8.59 dpt.

The eye-facing surface is a spherical surface with

    D.sub.2x =D.sub.2y =-2.00 dpt.

If such an ophthalmic lens has a diameter of 66 mm and a

mimimum edge thickness of 0.50 mm,

the maximum edge thickness is 2.83 mm

and the center thickness 8.09 mm

Thus the ophthalmic lens provides aspherical correction of 5.0. dpt and,without taking into account the refractive index gradient, a cylindricalcorrection of +2.00 dpt at an axial position of 0°. Additionalcyclindrical correction of +2.00 dpt at an axial position of 0° isproduced by the means of the one-dimensional course n(y) of therefractive index.

A comparison of the two invented ophthalmic lenses with a customary lensreveals the following:

The center thickness, i.e. the critical thickness in an ophthalmic lensof positive power, is reduced by approximately 75% and the maximum edgethickness even by 90%, without the aberrations worsening in thepreferred embodiment in which all of the cyclindrical correction isattained by the refractive index gradient. On the contrary the inventedophthalmic lens even has more favorable image properties than thecustomary toric lens with spherical main sections. In particular, thefoccusing error R never becomes positive and therefore can becompensated for by means of negligible adaption.

Like the invented preferred embodiment providing cylindrical correctionof +2.0 dpt, with this preferred embodiment it is also remarkablypossible to maintain specific marginal conditions for aberrations inaddition to meeting the requirements regarding center and edge thicknessdespite the use of an only one-dimensional gradient of the refractiveindex and consequently restricted possiblity of variation in correction:

In the preferred embodiment illustrated in FIGS. 19 to 24 the errorcorrection is designed in such a manner that for all the values of φ thefocussing error R <0 and for φ=90° astigmatism S' is approximately zeroup to the angles of vision σ≈30°.

The one-dimensional gradient of the refractive index for this preferredembodiment is also calculated with spline functions, the exact course isindicated in the partial FIGS. 20a and b. If the refractive index n(y)resulting with spline functions is appoximated with a Taylor series inthe region of the optical axis

    n(y)=n.sub.o +n.sub.2y *y.sup.2 +. . . ,

in the vicinty of the axis for the coefficient is yielded

    n.sub.2y =-3.314*10.sup.-4 [mm.sup.-2 ].

In the preferred embodiment in which the "entire cylindrical correction"is attained half by means of the "toric surface design" and half bymeans of the refractive index gradient, the center thickness, i.e. thecritical thickness in a ophthalmic lens of positive power, is, however,negligibly greater than in the first preferred embodiment, in which theentire cylindrical correction was attained by means of the refractiveindex gradient. Yet compared to the customary ophthalmic lens, it isreduced by approximately 22% and the maximum edge thickness even byapproximately 45%. In addition, the absolute values of the aberrationsS' and R are distinctly smaller than in the first preferred embodimentand in the customary ophthalmic lens. The negligible positive values ofR at φ≈0° is of no significance as the absolute value is very small.

With this preferred embodiment, too, it is possible despite theutilization of an only one-dimensional gradient of the refractive index,which only changes along the lower refracting main section and is mirrorsymmetrical to the plane of the second (other) main section andconsequently restricted possibilty of variation in correction, tomaintain specific marginal conditions for the aberrations in addition tomeeting requirements regarding center and edge thickness.

In the invented embodiment illustrated in FIGS. 25 to 30, the errorcorrection is designed in such a manner that the for φ=90° astigmatismS' is approximately zero up to the angles of vision σ=30°.

The one-dimensional gradient of the refractive index is also calculatedfor the second preferred embodiment for a cylindrical correction of +4.0dpt using spline functions, the exact course is indicated in the partialFIGS. 26a and b. If the refractive index n(y) resulting with the splinefunctions is approximated once more in the optical axis with a Taylorseries, for the coefficient n_(2y) is yielded

    n.sub.2y =-1.177*10.sup.-4 [mm.sup.-2 ].

In the preceding section the present invention has been described usingpreferred embodiments without the intention of limiting the scope of theoverall inventive concept - to utilize a gradient of the refractiveindex having a preferred direction in the direction of the critical mainsection:

There are, of course, many very varied possible modifications withinthis overall inventive concept:

By way of illustration, a refractive index course may be selected inwhich the refractive index is dependent on x and/or changes in the axialdirection, instead of the one-dimensional gradient used in the preferredembodiments, in which the refractive index is only dependent on y. Witha gradient like the former, aberrations in the peripheral regions andbetween the main sections can be further reduced. It is also possible toutilize an aspheric or toric lens, i.e. a lens having at least oneaspheric main section provided with a refractive index gradientaccording to the present invention, instead of a lens with sphericalsurfaces or spherical main sections. By this means it is also possibleto further reduce aberrations and/or the critical thickness as well asthe variation of the edge thicknesses.

In the illustrated preferred embodiments the refractive index changespractically up to the edge of the lens. However, it is also possible topermit only one variation of the refractive index up to the angle ofvision σ'≈30° and to hold the refractive index constant with largerangles of vision, thereby facilitating the manufacture of the lens,which is already much simplified compared to other proposals forrefractive index gradients due to only one-dimensional main variation.

Needless to say that in the case of other axial positions of the eye,for which an invented lens is to be employed, the selected main sectionsare to be appropriately modified from the illustrated preferredembodiments.

Furthermore, in the aforedescribed preferred embodiments, a gradient wasemployed which only changes along the critical main section and mirrorsymmetrically to the second main section. Naturally, it is also possibleto relinquish the mirror symmetry requirement for correction of theso-called "astigmatism obliqus" while taking into account the Listingprinciple and/or use in addition two-dimensional gradients.

Also the fact that all the preferred embodiments described in detail inthe foregoing are lenses of positive power is not to be construed as arestriction of the overall inventive concept. For an expert skilled inthe art it presents no difficulty to apply the technical principleshereof to lenses of negative power the edge thickness of which is to bereduced or to lenses in which one main section is of positive power andthe other of negative power and in which the center thickness and theedge thickness are to be reduced accordingly.

The invented ophthalmic lenses can be manufactured by means of one ofthe processes described in the published relative literature. In thismatter reference is made to the survey mentioned in the introductionhereto.

What I claim is:
 1. An ophthalmic lens for use in the correction ofastigmatism having two surfaces including a front surface and aneye-facing surface, wherein, in order to reduce one of a criticalthickness and a variation of an edge thickness along the circumferenceof said lens, the refractive index changes at least along a criticalmain section in such a manner that at least part of a cylindricalcorrection is attained by the variation of said refractive index.
 2. Anophthalmic lens according to claim 1, wherein said variation of therefractive index along said critical main section is mirror-symmetricalto the plane of an other non-critical main section.
 3. An ophthalmiclens according to claim 2, wherein said refractive index is constantalong surfaces which are parallel planes to said other main section. 4.An ophthalmic lens according to one of the claims 1 to 3, wherein for apredetermined range of cylindrical corrections, said cylindricalcorrection is attained solely by said variation of said refractiveindex.
 5. An ophthalmic lens according to claim 4, wherein both saidfront surface and said eye-facing surface are spherical surfaces.
 6. Anophthalmic lens according to claim 2 or 3 wherein at least one of saidtwo surfaces is a rotationally symmetrical aspheric surface, the courseof which reduces aberrrations at least along said other main section. 7.An ophthalmic lens according to one of the claims 1 to 3, wherein one ofsaid two surfaces is an atoric surface.
 8. An ophthalmic lens accordingto one of the claims 1 to 3, wherein in the description of therefractive index function n(y) using a Taylor series

    n(y)=n.sub.o +n.sub.2y *y.sup.2 +. . .

the following equation defines the coefficient n_(2y) mm⁻² :

    n.sub.2y =(1-d*D.sub.1y /n.sub.o)*D.sub.1y /(1-d*D.sub.1y /n.sub.o)-D.sub.1x /(1-d*D.sub.1x /n.sub.o)+D.sub.2y -D.sub.2x -Zy1/(2*d)

whereby: D_(1x) or y being the surface refractive value of said frontsurface in the x or y direction, D_(2x) or y the surface refractivevalue of said eye-facing surface in the x or y direction, n_(o) saidrefractive index in the optical axis, d said center thickness, and Zy1S'_(oy) -S'_(ox) (definition of the cylindrical correction).